I would rather have always have my tensor product look like $A\underset{R}{\otimes}B$ but still write $A\otimes_R B$. Is there a way to make this happen by some command in the preamble? (it's ok if it only works in display mode)

\bigotimes is a symbol that takes limits, so use that instead.
–
barbara beetonApr 16 '14 at 8:58

One would use that in the sense of \sum for addition. In math sometimes you have to specify over which ring one does the tensor product (of just two modules).
–
Peter PatztApr 16 '14 at 9:08

An idea I just had would be something like \renewcommand{\tensor}{\ensuremath\otimes\limits} but it does not work because \otimes is not a math operator.
–
Peter PatztApr 16 '14 at 9:16

you could then try \mathop{\opotimes}{$\otimes$} (i've forgotten which code says this takes limits, and i'm not sure this syntax is exactly correct either, but it's in the right direction). or \DeclareMathOperator from amsmath.
–
barbara beetonApr 16 '14 at 9:21

1 Answer
1

Perhaps you like the ring to go below the tensor product symbol, but typography doesn't. Here's why:

\documentclass{article}
\usepackage{amsmath}
\newcommand{\tens}[1]{%
\mathbin{\mathop{\otimes}\limits_{#1}}%
}
\begin{document}
Here is a tensor product $M\tens{R}N$, but note that
it will have a very bad influence on the spacing of
lines.
Here is a tensor product $M\tens{R}N$, but note that
it will have a very bad influence on the spacing of
lines.
Here is a tensor product $M\tens{R}N$, but note that
it will have a very bad influence on the spacing of
lines.
Here is a tensor product $M\tens{R}N$, but note that
it will have a very bad influence on the spacing of
lines.
Here is a tensor product $M\tens{R}N$, but note that
it will have a very bad influence on the spacing of
lines.
Here is a tensor product $M\tens{R}N$, but note that
it will have a very bad influence on the spacing of
lines.
\end{document}

A simple change will make what you perhaps prefer, but I'm not sure to like it very much.

\documentclass{article}
\usepackage{amsmath}
\newcommand{\tens}[1]{%
\mathbin{\mathop{\otimes}\displaylimits_{#1}}%
}
\begin{document}
Here is a tensor product $M\tens{R}N$, note that
it won't have a very bad influence on the spacing of
lines.
Here is a tensor product $M\tens{R}N$, note that
it won't have a very bad influence on the spacing of
lines.
Here is a tensor product $M\tens{R}N$, note that
it won't have a very bad influence on the spacing of
lines.
Here is a tensor product $M\tens{R}N$, note that
it won't have a very bad influence on the spacing of
lines.
Here is a tensor product $M\tens{R}N$, note that
it won't have a very bad influence on the spacing of
lines.
Here is a tensor product $M\tens{R}N$, note that
it won't have a very bad influence on the spacing of
lines.
\[
M\tens{R}N
\]
Here is a tensor product $M\tens{R}N$, note that
it won't have a very bad influence on the spacing of
lines.
\end{document}

@PeterPatzt I'll tell you that in my young years as a LaTeX user I had to use \otimes many times and I too wanted the ring below it; but I realized that it's not so nice, after all.
–
egregApr 16 '14 at 9:40